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On the fixed point index of iterates of planar homeomorphisms

Author: Morton Brown
Journal: Proc. Amer. Math. Soc. 108 (1990), 1109-1114
MSC: Primary 54H25; Secondary 55M20, 55M25, 57N05
MathSciNet review: 994772
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Abstract: If $ f$ is an orientation preserving homeomorphism of the plane with an isolated fixed point at the origin 0 and $ {\text{index(}}f,0{\text{) = }}p$, then $ {\text{index(}}{f^n}{\text{,0)}}$ is always well defined provided that $ p \ne 1$. In this case, for each $ n \ne 0$, $ {\text{index(}}{f^n}{\text{,0) = index(}}f,o{\text{) = }}p$. If $ {\text{index(}}f,0{\text{) = 1}}$, then there is an integer $ p$ (possibly $ p = 1$) such that for those values of $ n$ for which $ {\text{index(}}{f^n}{\text{,0)}}$ is defined (i.e 0 is an isolated fixed point of $ {f^n}$), $ {\text{index(}}{f^n}{\text{,0) = 1}}$ or $ {\text{index(}}{f^n}{\text{,0) = }}p$.

References [Enhancements On Off] (What's this?)

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Article copyright: © Copyright 1990 American Mathematical Society

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